The clearest a priori knowledge is proving non-existence through contradiction

Full Idea:
One proves non-existence (e.g. of round squares) by using logic to derive a contradiction from the concept; it is precisely here, in such proofs, that we find the clearest example of a priori knowledge.

If slowness is a property of walking rather than the walker, we must allow that events exist

Full Idea:
Once we conceded that Tom can walk slowly or quickly, and that the slowness and quickness is a property of the walking and not of Tom, we can hardly refrain from quantifying over events (such as 'a walking') in our ontology.

A reaction:
The mass-nouns are such things as earth, air, fire and water. This is a very interesting historical observation (cited by Laycock). Our obsession with identity seems tied to formal logic. There is a whole other worldview waiting out there.

There are the 'is' of predication (a function), the 'is' of identity (equals), and the 'is' of existence (quantifier)

Full Idea:
At least since Russell, one has routinely distinguished between the 'is' of predication ('Socrates is wise', Fx), the 'is' of identity ('Morning Star is Evening Star', =), and the 'is' of existence ('the cat is under the bed', Ex).

A reaction:
This seems horribly nitpicking to many people, but I love it - because it is just true, and it is a truth right at the basis of the confusions in our talk. Analytic philosophy forever! [P.S. 'Tiddles is a cat' - the 'is' membership]

Absolutists might accept that to exist is relative, but relative to what? How about relative to itself?

Full Idea:
With the thesis that to be as such is to be relative, the absolutist may be found to concur, but the issue turns on what it might be that a thing is supposed to be relative to. Why not itself?

Assertions about existence beyond experience can only be a priori synthetic

Full Idea:
No one thinks that the proposition that something exists that transcends all possible experience harbours a logical inconsistency. Its denial cannot therefore be an analytic proposition, so it must be synthetic, though only knowable on a priori grounds.

If we know truths about prime numbers, we seem to have synthetic a priori knowledge of Platonic objects

Full Idea:
Assume that we know to be true propositions of the form 'There are exactly x prime numbers between y and z', and synthetic a priori truths about Platonic objects are delivered to us on a silver platter.